### Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves

David Lannes (2008-2009)

Séminaire Équations aux dérivées partielles

Similarity:

This note is devoted to the study of a bi-fluid generalization of the nonlinear shallow-water equations. It describes the evolution of the interface between two fluids of different densities. In the case of a two-dimensional interface, this systems contains unexpected nonlocal terms (that are of course not present in the usual one-fluid shallow water equations). We show here how to derive this systems from the two-fluid Euler equations and then show that it is locally well-posed. ...